I'm sure there are things in analysis that some people find prettier than the Hahn-Banach theorem. But analysis is probably my weakest branch of mathematics, despite doing my PhD in Riemann surface stuff which is largely complex analysis. As a result, the Hahn-Banach theorem is about as far as I ever got in the subject. And even then I don't find the usual statement of it terribly intuitive. (I suspect an analyst would have trouble understanding why I could possibly fail to get it.)